Existence and uniqueness of a solution for a BVP from developmental biology

Recently, Sherrat [J. Appl. Math. 47, 147 (1991)] introduced a model for the behaviour of an epithelial sheet after a section of the sheet had been removed. Consideration of radially symmetric equilibria reduces the original PDE to an ODE boundary value problem. Sherratt employed formal perturbation analyses to produce an expansion for the solution by exploiting a small parameter ε. In this article the author gives a rigorous proof that, for each ε >0, a solution exists and that it is unique. This is achieved using a topological shooting argument. Also given are results concerning the physically relevant 'sharp edge' of the solution near the boundary.